In Exercises 1–10, find the dimensions of the given matrix, and identify the given entry.
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Chapter 4 Solutions
Finite Mathematics
- Let A = Find an invertible matrix X and a diagonal matrix D such that X-¹AX = D. 1.88 88 X = -8 0.5] -8-3 D=arrow_forwardHow many free variables does each augmented matrix have? a. Choose b. Choose c. Choose d. Choose v 04 1 2 000 1 0 100 10 0 1 0 0-8 000 0 000 0 0 1 0 0 10 -8 0 0 0 0 15-10 -8 00 0 0arrow_forwardSuppose A is a 2 x 2 matrix such that A and 1 A What is A-1?arrow_forward
- Exercise 2. Show that for any square matrices A, B, if A ~ B, then tr(A) tr(B). Hint: First show that tr(XY) = tr(Y X) for any m x n matrix X and any nx m matrix Y.arrow_forwardDetermine the dimension of the nullspace of the matrix [1 2 3 M 0 1 0 O 1 O 2 O 3arrow_forwardFor the matrix A below, if g(X)-X ²-4. What are the elements of g(A). :) 1. 2. A%3D 3. 4.arrow_forward
- Exercise 5H. Let X be a square matrix with real entries such that XTX = I. Argue that det(X) = +1.arrow_forwardUse the definition of the matrix exponential, given below, to compute eA. For any n x n matrix A, eAt = I + At + Aktk Aktk k! ... + +... 2! k! k=0 00 0 A = | 3 0 0 4 1 0 eAtarrow_forwardPage 4 of 5 MATH 209/ MATH 201 7. The rank of an identity matrix of order n is: A. n -1 B. n C. n+ 1 D. 0arrow_forward
- 3. Consider the matrix (in Matlab notation) A = [1, a; a, 1] where the value of a gets close to 1, i.e., a = 0.9; 0.99; 0.999, etc. Study how it maps the unit circle x, y = Ax.arrow_forwardFind a matrix S such that S? = A, if 1 15 1 0 16 209 O 225 A = | |arrow_forwardFind the transpose of the following: In all of the matrix calculations below, you must show your work! ⌈ 1 5 9 13 ⌉ | 2 4 10 14 | | 3 7 11 15 | ⌊ 4 8 12 16 ⌋ ⌈ 4 ⌉ | 3 | | 2 | ⌊ 1 ⌋arrow_forward
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning